LMFDB - Embedded newform 22.6.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,6,Mod(1,22)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("22.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	22.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$3.52844403589$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	22.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$

$=$

$q+4.00000 q^{2} -29.0000 q^{3} +16.0000 q^{4} -31.0000 q^{5} -116.000 q^{6} -230.000 q^{7} +64.0000 q^{8} +598.000 q^{9} +O(q^{10})$

\(q+4.00000 q^{2} -29.0000 q^{3} +16.0000 q^{4} -31.0000 q^{5} -116.000 q^{6} -230.000 q^{7} +64.0000 q^{8} +598.000 q^{9} -124.000 q^{10} +121.000 q^{11} -464.000 q^{12} +112.000 q^{13} -920.000 q^{14} +899.000 q^{15} +256.000 q^{16} -1142.00 q^{17} +2392.00 q^{18} -612.000 q^{19} -496.000 q^{20} +6670.00 q^{21} +484.000 q^{22} -1941.00 q^{23} -1856.00 q^{24} -2164.00 q^{25} +448.000 q^{26} -10295.0 q^{27} -3680.00 q^{28} +1192.00 q^{29} +3596.00 q^{30} -1037.00 q^{31} +1024.00 q^{32} -3509.00 q^{33} -4568.00 q^{34} +7130.00 q^{35} +9568.00 q^{36} +8083.00 q^{37} -2448.00 q^{38} -3248.00 q^{39} -1984.00 q^{40} -10444.0 q^{41} +26680.0 q^{42} +58.0000 q^{43} +1936.00 q^{44} -18538.0 q^{45} -7764.00 q^{46} +8656.00 q^{47} -7424.00 q^{48} +36093.0 q^{49} -8656.00 q^{50} +33118.0 q^{51} +1792.00 q^{52} -20318.0 q^{53} -41180.0 q^{54} -3751.00 q^{55} -14720.0 q^{56} +17748.0 q^{57} +4768.00 q^{58} -21351.0 q^{59} +14384.0 q^{60} +47044.0 q^{61} -4148.00 q^{62} -137540. q^{63} +4096.00 q^{64} -3472.00 q^{65} -14036.0 q^{66} +48093.0 q^{67} -18272.0 q^{68} +56289.0 q^{69} +28520.0 q^{70} -24967.0 q^{71} +38272.0 q^{72} -42288.0 q^{73} +32332.0 q^{74} +62756.0 q^{75} -9792.00 q^{76} -27830.0 q^{77} -12992.0 q^{78} -72410.0 q^{79} -7936.00 q^{80} +153241. q^{81} -41776.0 q^{82} -15806.0 q^{83} +106720. q^{84} +35402.0 q^{85} +232.000 q^{86} -34568.0 q^{87} +7744.00 q^{88} -114761. q^{89} -74152.0 q^{90} -25760.0 q^{91} -31056.0 q^{92} +30073.0 q^{93} +34624.0 q^{94} +18972.0 q^{95} -29696.0 q^{96} -5159.00 q^{97} +144372. q^{98} +72358.0 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	−29.0000	−1.86035	−0.930175	−	0.367115i	$-0.880345\pi$
$3$	−29.0000	−1.86035	−0.930175	+	0.367115i	$0.880345\pi$
$4$	16.0000	0.500000
$5$	−31.0000	−0.554545	−0.277272	−	0.960791i	$-0.589430\pi$
$5$	−31.0000	−0.554545	−0.277272	+	0.960791i	$0.589430\pi$
$6$	−116.000	−1.31547
$7$	−230.000	−1.77412	−0.887059	−	0.461655i	$-0.847256\pi$
$7$	−230.000	−1.77412	−0.887059	+	0.461655i	$0.847256\pi$
$8$	64.0000	0.353553
$9$	598.000	2.46091
$10$	−124.000	−0.392122
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−464.000	−0.930175
$13$	112.000	0.183806	0.0919030	−	0.995768i	$-0.470705\pi$
$13$	112.000	0.183806	0.0919030	+	0.995768i	$0.470705\pi$
$14$	−920.000	−1.25449
$15$	899.000	1.03165
$16$	256.000	0.250000
$17$	−1142.00	−0.958393	−0.479197	−	0.877708i	$-0.659072\pi$
$17$	−1142.00	−0.958393	−0.479197	+	0.877708i	$0.659072\pi$
$18$	2392.00	1.74012
$19$	−612.000	−0.388926	−0.194463	−	0.980910i	$-0.562296\pi$
$19$	−612.000	−0.388926	−0.194463	+	0.980910i	$0.562296\pi$
$20$	−496.000	−0.277272
$21$	6670.00	3.30048
$22$	484.000	0.213201
$23$	−1941.00	−0.765078	−0.382539	−	0.923939i	$-0.624950\pi$
$23$	−1941.00	−0.765078	−0.382539	+	0.923939i	$0.624950\pi$
$24$	−1856.00	−0.657733
$25$	−2164.00	−0.692480
$26$	448.000	0.129970
$27$	−10295.0	−2.71780
$28$	−3680.00	−0.887059
$29$	1192.00	0.263197	0.131599	−	0.991303i	$-0.457989\pi$
$29$	1192.00	0.263197	0.131599	+	0.991303i	$0.457989\pi$
$30$	3596.00	0.729485
$31$	−1037.00	−0.193809	−0.0969046	−	0.995294i	$-0.530894\pi$
$31$	−1037.00	−0.193809	−0.0969046	+	0.995294i	$0.530894\pi$
$32$	1024.00	0.176777
$33$	−3509.00	−0.560917
$34$	−4568.00	−0.677686
$35$	7130.00	0.983829
$36$	9568.00	1.23045
$37$	8083.00	0.970663	0.485331	−	0.874330i	$-0.338699\pi$
$37$	8083.00	0.970663	0.485331	+	0.874330i	$0.338699\pi$
$38$	−2448.00	−0.275012
$39$	−3248.00	−0.341944
$40$	−1984.00	−0.196061
$41$	−10444.0	−0.970303	−0.485151	−	0.874430i	$-0.661235\pi$
$41$	−10444.0	−0.970303	−0.485151	+	0.874430i	$0.661235\pi$
$42$	26680.0	2.33379
$43$	58.0000	0.00478362	0.00239181	−	0.999997i	$-0.499239\pi$
$43$	58.0000	0.00478362	0.00239181	+	0.999997i	$0.499239\pi$
$44$	1936.00	0.150756
$45$	−18538.0	−1.36468
$46$	−7764.00	−0.540992
$47$	8656.00	0.571574	0.285787	−	0.958293i	$-0.407745\pi$
$47$	8656.00	0.571574	0.285787	+	0.958293i	$0.407745\pi$
$48$	−7424.00	−0.465088
$49$	36093.0	2.14750
$50$	−8656.00	−0.489657
$51$	33118.0	1.78295
$52$	1792.00	0.0919030
$53$	−20318.0	−0.993554	−0.496777	−	0.867878i	$-0.665483\pi$
$53$	−20318.0	−0.993554	−0.496777	+	0.867878i	$0.665483\pi$
$54$	−41180.0	−1.92177
$55$	−3751.00	−0.167202
$56$	−14720.0	−0.627246
$57$	17748.0	0.723540
$58$	4768.00	0.186109
$59$	−21351.0	−0.798524	−0.399262	−	0.916837i	$-0.630734\pi$
$59$	−21351.0	−0.798524	−0.399262	+	0.916837i	$0.630734\pi$
$60$	14384.0	0.515824
$61$	47044.0	1.61875	0.809375	−	0.587293i	$-0.199806\pi$
$61$	47044.0	1.61875	0.809375	+	0.587293i	$0.199806\pi$
$62$	−4148.00	−0.137044
$63$	−137540.	−4.36594
$64$	4096.00	0.125000
$65$	−3472.00	−0.101929
$66$	−14036.0	−0.396628
$67$	48093.0	1.30887	0.654433	−	0.756120i	$-0.272908\pi$
$67$	48093.0	1.30887	0.654433	+	0.756120i	$0.272908\pi$
$68$	−18272.0	−0.479197
$69$	56289.0	1.42331
$70$	28520.0	0.695672
$71$	−24967.0	−0.587788	−0.293894	−	0.955838i	$-0.594951\pi$
$71$	−24967.0	−0.587788	−0.293894	+	0.955838i	$0.594951\pi$
$72$	38272.0	0.870061
$73$	−42288.0	−0.928774	−0.464387	−	0.885632i	$-0.653725\pi$
$73$	−42288.0	−0.928774	−0.464387	+	0.885632i	$0.653725\pi$
$74$	32332.0	0.686362
$75$	62756.0	1.28826
$76$	−9792.00	−0.194463
$77$	−27830.0	−0.534917
$78$	−12992.0	−0.241791
$79$	−72410.0	−1.30536	−0.652681	−	0.757633i	$-0.726356\pi$
$79$	−72410.0	−1.30536	−0.652681	+	0.757633i	$0.726356\pi$
$80$	−7936.00	−0.138636
$81$	153241.	2.59515
$82$	−41776.0	−0.686108
$83$	−15806.0	−0.251841	−0.125921	−	0.992040i	$-0.540188\pi$
$83$	−15806.0	−0.251841	−0.125921	+	0.992040i	$0.540188\pi$
$84$	106720.	1.65024
$85$	35402.0	0.531472
$86$	232.000	0.00338253
$87$	−34568.0	−0.489639
$88$	7744.00	0.106600
$89$	−114761.	−1.53575	−0.767873	−	0.640602i	$-0.778685\pi$
$89$	−114761.	−1.53575	−0.767873	+	0.640602i	$0.778685\pi$
$90$	−74152.0	−0.964976
$91$	−25760.0	−0.326094
$92$	−31056.0	−0.382539
$93$	30073.0	0.360553
$94$	34624.0	0.404164
$95$	18972.0	0.215677
$96$	−29696.0	−0.328867
$97$	−5159.00	−0.0556719	−0.0278360	−	0.999613i	$-0.508862\pi$
$97$	−5159.00	−0.0556719	−0.0278360	+	0.999613i	$0.508862\pi$
$98$	144372.	1.51851
$99$	72358.0	0.741991
$100$	−34624.0	−0.346240
$101$	−61426.0	−0.599168	−0.299584	−	0.954070i	$-0.596848\pi$
$101$	−61426.0	−0.599168	−0.299584	+	0.954070i	$0.596848\pi$
$102$	132472.	1.26073
$103$	185896.	1.72654	0.863271	−	0.504741i	$-0.168412\pi$
$103$	185896.	1.72654	0.863271	+	0.504741i	$0.168412\pi$
$104$	7168.00	0.0649852
$105$	−206770.	−1.83027
$106$	−81272.0	−0.702548
$107$	−23970.0	−0.202399	−0.101200	−	0.994866i	$-0.532268\pi$
$107$	−23970.0	−0.202399	−0.101200	+	0.994866i	$0.532268\pi$
$108$	−164720.	−1.35890
$109$	−56326.0	−0.454091	−0.227045	−	0.973884i	$-0.572907\pi$
$109$	−56326.0	−0.454091	−0.227045	+	0.973884i	$0.572907\pi$
$110$	−15004.0	−0.118229
$111$	−234407.	−1.80577
$112$	−58880.0	−0.443530
$113$	−261903.	−1.92950	−0.964749	−	0.263171i	$-0.915231\pi$
$113$	−261903.	−1.92950	−0.964749	+	0.263171i	$0.915231\pi$
$114$	70992.0	0.511620
$115$	60171.0	0.424270
$116$	19072.0	0.131599
$117$	66976.0	0.452329
$118$	−85404.0	−0.564642
$119$	262660.	1.70030
$120$	57536.0	0.364743
$121$	14641.0	0.0909091
$122$	188176.	1.14463
$123$	302876.	1.80510
$124$	−16592.0	−0.0969046
$125$	163959.	0.938556
$126$	−550160.	−3.08718
$127$	87404.0	0.480864	0.240432	−	0.970666i	$-0.422711\pi$
$127$	87404.0	0.480864	0.240432	+	0.970666i	$0.422711\pi$
$128$	16384.0	0.0883883
$129$	−1682.00	−0.00889922
$130$	−13888.0	−0.0720744
$131$	265122.	1.34979	0.674897	−	0.737912i	$-0.264188\pi$
$131$	265122.	1.34979	0.674897	+	0.737912i	$0.264188\pi$
$132$	−56144.0	−0.280458
$133$	140760.	0.690002
$134$	192372.	0.925507
$135$	319145.	1.50714
$136$	−73088.0	−0.338843
$137$	245857.	1.11913	0.559566	−	0.828786i	$-0.310968\pi$
$137$	245857.	1.11913	0.559566	+	0.828786i	$0.310968\pi$
$138$	225156.	1.00644
$139$	−363594.	−1.59617	−0.798086	−	0.602544i	$-0.794154\pi$
$139$	−363594.	−1.59617	−0.798086	+	0.602544i	$0.794154\pi$
$140$	114080.	0.491914
$141$	−251024.	−1.06333
$142$	−99868.0	−0.415629
$143$	13552.0	0.0554196
$144$	153088.	0.615226
$145$	−36952.0	−0.145955
$146$	−169152.	−0.656742
$147$	−1.04670e6	−3.99510
$148$	129328.	0.485331
$149$	−55750.0	−0.205721	−0.102861	−	0.994696i	$-0.532800\pi$
$149$	−55750.0	−0.205721	−0.102861	+	0.994696i	$0.532800\pi$
$150$	251024.	0.910934
$151$	65642.0	0.234282	0.117141	−	0.993115i	$-0.462627\pi$
$151$	65642.0	0.234282	0.117141	+	0.993115i	$0.462627\pi$
$152$	−39168.0	−0.137506
$153$	−682916.	−2.35852
$154$	−111320.	−0.378243
$155$	32147.0	0.107476
$156$	−51968.0	−0.170972
$157$	−275367.	−0.891585	−0.445793	−	0.895136i	$-0.647078\pi$
$157$	−275367.	−0.891585	−0.445793	+	0.895136i	$0.647078\pi$
$158$	−289640.	−0.923030
$159$	589222.	1.84836
$160$	−31744.0	−0.0980306
$161$	446430.	1.35734
$162$	612964.	1.83505
$163$	291940.	0.860646	0.430323	−	0.902675i	$-0.358400\pi$
$163$	291940.	0.860646	0.430323	+	0.902675i	$0.358400\pi$
$164$	−167104.	−0.485151
$165$	108779.	0.311054
$166$	−63224.0	−0.178079
$167$	−337344.	−0.936013	−0.468006	−	0.883725i	$-0.655028\pi$
$167$	−337344.	−0.936013	−0.468006	+	0.883725i	$0.655028\pi$
$168$	426880.	1.16690
$169$	−358749.	−0.966215
$170$	141608.	0.375808
$171$	−365976.	−0.957111
$172$	928.000	0.00239181
$173$	−116742.	−0.296560	−0.148280	−	0.988945i	$-0.547374\pi$
$173$	−116742.	−0.296560	−0.148280	+	0.988945i	$0.547374\pi$
$174$	−138272.	−0.346227
$175$	497720.	1.22854
$176$	30976.0	0.0753778
$177$	619179.	1.48554
$178$	−459044.	−1.08594
$179$	−19107.0	−0.0445718	−0.0222859	−	0.999752i	$-0.507094\pi$
$179$	−19107.0	−0.0445718	−0.0222859	+	0.999752i	$0.507094\pi$
$180$	−296608.	−0.682341
$181$	−16177.0	−0.0367030	−0.0183515	−	0.999832i	$-0.505842\pi$
$181$	−16177.0	−0.0367030	−0.0183515	+	0.999832i	$0.505842\pi$
$182$	−103040.	−0.230583
$183$	−1.36428e6	−3.01144
$184$	−124224.	−0.270496
$185$	−250573.	−0.538276
$186$	120292.	0.254950
$187$	−138182.	−0.288966
$188$	138496.	0.285787
$189$	2.36785e6	4.82169
$190$	75888.0	0.152507
$191$	685333.	1.35931	0.679655	−	0.733532i	$-0.262130\pi$
$191$	685333.	1.35931	0.679655	+	0.733532i	$0.262130\pi$
$192$	−118784.	−0.232544
$193$	−309292.	−0.597689	−0.298845	−	0.954302i	$-0.596601\pi$
$193$	−309292.	−0.597689	−0.298845	+	0.954302i	$0.596601\pi$
$194$	−20636.0	−0.0393660
$195$	100688.	0.189623
$196$	577488.	1.07375
$197$	−120930.	−0.222008	−0.111004	−	0.993820i	$-0.535407\pi$
$197$	−120930.	−0.222008	−0.111004	+	0.993820i	$0.535407\pi$
$198$	289432.	0.524667
$199$	915536.	1.63886	0.819432	−	0.573177i	$-0.194289\pi$
$199$	915536.	1.63886	0.819432	+	0.573177i	$0.194289\pi$
$200$	−138496.	−0.244829
$201$	−1.39470e6	−2.43495
$202$	−245704.	−0.423676
$203$	−274160.	−0.466943
$204$	529888.	0.891474
$205$	323764.	0.538076
$206$	743584.	1.22085
$207$	−1.16072e6	−1.88279
$208$	28672.0	0.0459515
$209$	−74052.0	−0.117266
$210$	−827080.	−1.29419
$211$	−134580.	−0.208101	−0.104051	−	0.994572i	$-0.533180\pi$
$211$	−134580.	−0.208101	−0.104051	+	0.994572i	$0.533180\pi$
$212$	−325088.	−0.496777
$213$	724043.	1.09349
$214$	−95880.0	−0.143118
$215$	−1798.00	−0.00265273
$216$	−658880.	−0.960886
$217$	238510.	0.343841
$218$	−225304.	−0.321091
$219$	1.22635e6	1.72785
$220$	−60016.0	−0.0836008
$221$	−127904.	−0.176158
$222$	−937628.	−1.27687
$223$	468839.	0.631337	0.315669	−	0.948869i	$-0.397771\pi$
$223$	468839.	0.631337	0.315669	+	0.948869i	$0.397771\pi$
$224$	−235520.	−0.313623
$225$	−1.29407e6	−1.70413
$226$	−1.04761e6	−1.36436
$227$	275022.	0.354244	0.177122	−	0.984189i	$-0.443321\pi$
$227$	275022.	0.354244	0.177122	+	0.984189i	$0.443321\pi$
$228$	283968.	0.361770
$229$	−642281.	−0.809350	−0.404675	−	0.914461i	$-0.632615\pi$
$229$	−642281.	−0.809350	−0.404675	+	0.914461i	$0.632615\pi$
$230$	240684.	0.300004
$231$	807070.	0.995133
$232$	76288.0	0.0930543
$233$	−1.50485e6	−1.81595	−0.907973	−	0.419029i	$-0.862371\pi$
$233$	−1.50485e6	−1.81595	−0.907973	+	0.419029i	$0.862371\pi$
$234$	267904.	0.319845
$235$	−268336.	−0.316964
$236$	−341616.	−0.399262
$237$	2.09989e6	2.42843
$238$	1.05064e6	1.20230
$239$	−304694.	−0.345040	−0.172520	−	0.985006i	$-0.555191\pi$
$239$	−304694.	−0.345040	−0.172520	+	0.985006i	$0.555191\pi$
$240$	230144.	0.257912
$241$	1.27181e6	1.41052	0.705260	−	0.708949i	$-0.250830\pi$
$241$	1.27181e6	1.41052	0.705260	+	0.708949i	$0.250830\pi$
$242$	58564.0	0.0642824
$243$	−1.94230e6	−2.11009
$244$	752704.	0.809375
$245$	−1.11888e6	−1.19088
$246$	1.21150e6	1.27640
$247$	−68544.0	−0.0714870
$248$	−66368.0	−0.0685219
$249$	458374.	0.468513
$250$	655836.	0.663659
$251$	629965.	0.631149	0.315575	−	0.948901i	$-0.397803\pi$
$251$	629965.	0.631149	0.315575	+	0.948901i	$0.397803\pi$
$252$	−2.20064e6	−2.18297
$253$	−234861.	−0.230680
$254$	349616.	0.340022
$255$	−1.02666e6	−0.988725
$256$	65536.0	0.0625000
$257$	544086.	0.513848	0.256924	−	0.966432i	$-0.417291\pi$
$257$	544086.	0.513848	0.256924	+	0.966432i	$0.417291\pi$
$258$	−6728.00	−0.00629270
$259$	−1.85909e6	−1.72207
$260$	−55552.0	−0.0509643
$261$	712816.	0.647703
$262$	1.06049e6	0.954449
$263$	−1.98933e6	−1.77345	−0.886724	−	0.462300i	$-0.847024\pi$
$263$	−1.98933e6	−1.77345	−0.886724	+	0.462300i	$0.847024\pi$
$264$	−224576.	−0.198314
$265$	629858.	0.550970
$266$	563040.	0.487905
$267$	3.32807e6	2.85703
$268$	769488.	0.654433
$269$	1.75446e6	1.47830	0.739149	−	0.673541i	$-0.235228\pi$
$269$	1.75446e6	1.47830	0.739149	+	0.673541i	$0.235228\pi$
$270$	1.27658e6	1.06571
$271$	−1.65824e6	−1.37159	−0.685795	−	0.727795i	$-0.740545\pi$
$271$	−1.65824e6	−1.37159	−0.685795	+	0.727795i	$0.740545\pi$
$272$	−292352.	−0.239598
$273$	747040.	0.606649
$274$	983428.	0.791346
$275$	−261844.	−0.208791
$276$	900624.	0.711657
$277$	−42634.0	−0.0333854	−0.0166927	−	0.999861i	$-0.505314\pi$
$277$	−42634.0	−0.0333854	−0.0166927	+	0.999861i	$0.505314\pi$
$278$	−1.45438e6	−1.12866
$279$	−620126.	−0.476946
$280$	456320.	0.347836
$281$	319510.	0.241390	0.120695	−	0.992690i	$-0.461488\pi$
$281$	319510.	0.241390	0.120695	+	0.992690i	$0.461488\pi$
$282$	−1.00410e6	−0.751887
$283$	−2.02735e6	−1.50474	−0.752371	−	0.658739i	$-0.771090\pi$
$283$	−2.02735e6	−1.50474	−0.752371	+	0.658739i	$0.771090\pi$
$284$	−399472.	−0.293894
$285$	−550188.	−0.401235
$286$	54208.0	0.0391876
$287$	2.40212e6	1.72143
$288$	612352.	0.435031
$289$	−115693.	−0.0814821
$290$	−147808.	−0.103206
$291$	149611.	0.103569
$292$	−676608.	−0.464387
$293$	718844.	0.489177	0.244588	−	0.969627i	$-0.421347\pi$
$293$	718844.	0.489177	0.244588	+	0.969627i	$0.421347\pi$
$294$	−4.18679e6	−2.82496
$295$	661881.	0.442818
$296$	517312.	0.343181
$297$	−1.24570e6	−0.819446
$298$	−223000.	−0.145467
$299$	−217392.	−0.140626
$300$	1.00410e6	0.644128
$301$	−13340.0	−0.00848671
$302$	262568.	0.165663
$303$	1.78135e6	1.11466
$304$	−156672.	−0.0972316
$305$	−1.45836e6	−0.897669
$306$	−2.73166e6	−1.66772
$307$	−1.98142e6	−1.19986	−0.599930	−	0.800052i	$-0.704805\pi$
$307$	−1.98142e6	−1.19986	−0.599930	+	0.800052i	$0.704805\pi$
$308$	−445280.	−0.267458
$309$	−5.39098e6	−3.21197
$310$	128588.	0.0759970
$311$	−1.51030e6	−0.885446	−0.442723	−	0.896658i	$-0.645988\pi$
$311$	−1.51030e6	−0.885446	−0.442723	+	0.896658i	$0.645988\pi$
$312$	−207872.	−0.120895
$313$	2.00092e6	1.15443	0.577216	−	0.816591i	$-0.304139\pi$
$313$	2.00092e6	1.15443	0.577216	+	0.816591i	$0.304139\pi$
$314$	−1.10147e6	−0.630446
$315$	4.26374e6	2.42111
$316$	−1.15856e6	−0.652681
$317$	−259331.	−0.144946	−0.0724730	−	0.997370i	$-0.523089\pi$
$317$	−259331.	−0.144946	−0.0724730	+	0.997370i	$0.523089\pi$
$318$	2.35689e6	1.30699
$319$	144232.	0.0793569
$320$	−126976.	−0.0693181
$321$	695130.	0.376533
$322$	1.78572e6	0.959784
$323$	698904.	0.372744
$324$	2.45186e6	1.29757
$325$	−242368.	−0.127282
$326$	1.16776e6	0.608569
$327$	1.63345e6	0.844768
$328$	−668416.	−0.343054
$329$	−1.99088e6	−1.01404
$330$	435116.	0.219948
$331$	51203.0	0.0256877	0.0128439	−	0.999918i	$-0.495912\pi$
$331$	51203.0	0.0256877	0.0128439	+	0.999918i	$0.495912\pi$
$332$	−252896.	−0.125921
$333$	4.83363e6	2.38871
$334$	−1.34938e6	−0.661861
$335$	−1.49088e6	−0.725824
$336$	1.70752e6	0.825121
$337$	266870.	0.128004	0.0640022	−	0.997950i	$-0.479614\pi$
$337$	266870.	0.128004	0.0640022	+	0.997950i	$0.479614\pi$
$338$	−1.43500e6	−0.683217
$339$	7.59519e6	3.58954
$340$	566432.	0.265736
$341$	−125477.	−0.0584357
$342$	−1.46390e6	−0.676780
$343$	−4.43578e6	−2.03580
$344$	3712.00	0.00169127
$345$	−1.74496e6	−0.789292
$346$	−466968.	−0.209699
$347$	622800.	0.277667	0.138834	−	0.990316i	$-0.455665\pi$
$347$	622800.	0.277667	0.138834	+	0.990316i	$0.455665\pi$
$348$	−553088.	−0.244820
$349$	2.43649e6	1.07078	0.535391	−	0.844604i	$-0.320164\pi$
$349$	2.43649e6	1.07078	0.535391	+	0.844604i	$0.320164\pi$
$350$	1.99088e6	0.868710
$351$	−1.15304e6	−0.499547
$352$	123904.	0.0533002
$353$	1.55957e6	0.666144	0.333072	−	0.942901i	$-0.391915\pi$
$353$	1.55957e6	0.666144	0.333072	+	0.942901i	$0.391915\pi$
$354$	2.47672e6	1.05043
$355$	773977.	0.325955
$356$	−1.83618e6	−0.767873
$357$	−7.61714e6	−3.16316
$358$	−76428.0	−0.0315170
$359$	1.91961e6	0.786098	0.393049	−	0.919518i	$-0.371420\pi$
$359$	1.91961e6	0.786098	0.393049	+	0.919518i	$0.371420\pi$
$360$	−1.18643e6	−0.482488
$361$	−2.10156e6	−0.848736
$362$	−64708.0	−0.0259529
$363$	−424589.	−0.169123
$364$	−412160.	−0.163047
$365$	1.31093e6	0.515047
$366$	−5.45710e6	−2.12941
$367$	3.61225e6	1.39995	0.699975	−	0.714167i	$-0.253194\pi$
$367$	3.61225e6	1.39995	0.699975	+	0.714167i	$0.253194\pi$
$368$	−496896.	−0.191270
$369$	−6.24551e6	−2.38782
$370$	−1.00229e6	−0.380619
$371$	4.67314e6	1.76268
$372$	481168.	0.180277
$373$	3.93968e6	1.46619	0.733093	−	0.680128i	$-0.238076\pi$
$373$	3.93968e6	1.46619	0.733093	+	0.680128i	$0.238076\pi$
$374$	−552728.	−0.204330
$375$	−4.75481e6	−1.74604
$376$	553984.	0.202082
$377$	133504.	0.0483772
$378$	9.47140e6	3.40945
$379$	−2.18829e6	−0.782540	−0.391270	−	0.920276i	$-0.627964\pi$
$379$	−2.18829e6	−0.782540	−0.391270	+	0.920276i	$0.627964\pi$
$380$	303552.	0.107839
$381$	−2.53472e6	−0.894575
$382$	2.74133e6	0.961177
$383$	768387.	0.267660	0.133830	−	0.991004i	$-0.457272\pi$
$383$	768387.	0.267660	0.133830	+	0.991004i	$0.457272\pi$
$384$	−475136.	−0.164433
$385$	862730.	0.296635
$386$	−1.23717e6	−0.422630
$387$	34684.0	0.0117720
$388$	−82544.0	−0.0278360
$389$	324313.	0.108665	0.0543326	−	0.998523i	$-0.482697\pi$
$389$	324313.	0.108665	0.0543326	+	0.998523i	$0.482697\pi$
$390$	402752.	0.134084
$391$	2.21662e6	0.733246
$392$	2.30995e6	0.759255
$393$	−7.68854e6	−2.51109
$394$	−483720.	−0.156983
$395$	2.24471e6	0.723882
$396$	1.15773e6	0.370995
$397$	334758.	0.106599	0.0532997	−	0.998579i	$-0.483026\pi$
$397$	334758.	0.106599	0.0532997	+	0.998579i	$0.483026\pi$
$398$	3.66214e6	1.15885
$399$	−4.08204e6	−1.28365
$400$	−553984.	−0.173120
$401$	−902022.	−0.280128	−0.140064	−	0.990142i	$-0.544731\pi$
$401$	−902022.	−0.280128	−0.140064	+	0.990142i	$0.544731\pi$
$402$	−5.57879e6	−1.72177
$403$	−116144.	−0.0356233
$404$	−982816.	−0.299584
$405$	−4.75047e6	−1.43913
$406$	−1.09664e6	−0.330179
$407$	978043.	0.292666
$408$	2.11955e6	0.630367
$409$	−5.00457e6	−1.47931	−0.739654	−	0.672987i	$-0.765011\pi$
$409$	−5.00457e6	−1.47931	−0.739654	+	0.672987i	$0.765011\pi$
$410$	1.29506e6	0.380477
$411$	−7.12985e6	−2.08198
$412$	2.97434e6	0.863271
$413$	4.91073e6	1.41668
$414$	−4.64287e6	−1.33133
$415$	489986.	0.139657
$416$	114688.	0.0324926
$417$	1.05442e7	2.96944
$418$	−296208.	−0.0829194
$419$	−3.00124e6	−0.835151	−0.417576	−	0.908642i	$-0.637120\pi$
$419$	−3.00124e6	−0.835151	−0.417576	+	0.908642i	$0.637120\pi$
$420$	−3.30832e6	−0.915133
$421$	4.56224e6	1.25451	0.627253	−	0.778816i	$-0.284179\pi$
$421$	4.56224e6	1.25451	0.627253	+	0.778816i	$0.284179\pi$
$422$	−538320.	−0.147150
$423$	5.17629e6	1.40659
$424$	−1.30035e6	−0.351274
$425$	2.47129e6	0.663668
$426$	2.89617e6	0.773215
$427$	−1.08201e7	−2.87185
$428$	−383520.	−0.101200
$429$	−393008.	−0.103100
$430$	−7192.00	−0.00187577
$431$	4.89783e6	1.27002	0.635009	−	0.772504i	$-0.280996\pi$
$431$	4.89783e6	1.27002	0.635009	+	0.772504i	$0.280996\pi$
$432$	−2.63552e6	−0.679449
$433$	6.72876e6	1.72471	0.862353	−	0.506307i	$-0.168990\pi$
$433$	6.72876e6	1.72471	0.862353	+	0.506307i	$0.168990\pi$
$434$	954040.	0.243132
$435$	1.07161e6	0.271527
$436$	−901216.	−0.227045
$437$	1.18789e6	0.297559
$438$	4.90541e6	1.22177
$439$	−3.35034e6	−0.829711	−0.414856	−	0.909887i	$-0.636168\pi$
$439$	−3.35034e6	−0.829711	−0.414856	+	0.909887i	$0.636168\pi$
$440$	−240064.	−0.0591147
$441$	2.15836e7	5.28479
$442$	−511616.	−0.124563
$443$	−7.12434e6	−1.72479	−0.862394	−	0.506238i	$-0.831036\pi$
$443$	−7.12434e6	−1.72479	−0.862394	+	0.506238i	$0.831036\pi$
$444$	−3.75051e6	−0.902886
$445$	3.55759e6	0.851640
$446$	1.87536e6	0.446423
$447$	1.61675e6	0.382714
$448$	−942080.	−0.221765
$449$	−2.70928e6	−0.634218	−0.317109	−	0.948389i	$-0.602712\pi$
$449$	−2.70928e6	−0.634218	−0.317109	+	0.948389i	$0.602712\pi$
$450$	−5.17629e6	−1.20500
$451$	−1.26372e6	−0.292557
$452$	−4.19045e6	−0.964749
$453$	−1.90362e6	−0.435847
$454$	1.10009e6	0.250489
$455$	798560.	0.180834
$456$	1.13587e6	0.255810
$457$	2.41361e6	0.540601	0.270301	−	0.962776i	$-0.412877\pi$
$457$	2.41361e6	0.540601	0.270301	+	0.962776i	$0.412877\pi$
$458$	−2.56912e6	−0.572297
$459$	1.17569e7	2.60472
$460$	962736.	0.212135
$461$	−6.56065e6	−1.43779	−0.718894	−	0.695120i	$-0.755351\pi$
$461$	−6.56065e6	−1.43779	−0.718894	+	0.695120i	$0.755351\pi$
$462$	3.22828e6	0.703665
$463$	−4.72421e6	−1.02418	−0.512090	−	0.858932i	$-0.671129\pi$
$463$	−4.72421e6	−1.02418	−0.512090	+	0.858932i	$0.671129\pi$
$464$	305152.	0.0657993
$465$	−932263.	−0.199943
$466$	−6.01939e6	−1.28407
$467$	−2.28444e6	−0.484716	−0.242358	−	0.970187i	$-0.577921\pi$
$467$	−2.28444e6	−0.484716	−0.242358	+	0.970187i	$0.577921\pi$
$468$	1.07162e6	0.226165
$469$	−1.10614e7	−2.32208
$470$	−1.07334e6	−0.224127
$471$	7.98564e6	1.65866
$472$	−1.36646e6	−0.282321
$473$	7018.00	0.00144232
$474$	8.39956e6	1.71716
$475$	1.32437e6	0.269324
$476$	4.20256e6	0.850152
$477$	−1.21502e7	−2.44504
$478$	−1.21878e6	−0.243980
$479$	951544.	0.189492	0.0947458	−	0.995501i	$-0.469796\pi$
$479$	951544.	0.189492	0.0947458	+	0.995501i	$0.469796\pi$
$480$	920576.	0.182371
$481$	905296.	0.178414
$482$	5.08723e6	0.997388
$483$	−1.29465e7	−2.52513
$484$	234256.	0.0454545
$485$	159929.	0.0308726
$486$	−7.76922e6	−1.49206
$487$	3.51484e6	0.671558	0.335779	−	0.941941i	$-0.391000\pi$
$487$	3.51484e6	0.671558	0.335779	+	0.941941i	$0.391000\pi$
$488$	3.01082e6	0.572314
$489$	−8.46626e6	−1.60110
$490$	−4.47553e6	−0.842082
$491$	−5.78719e6	−1.08334	−0.541669	−	0.840592i	$-0.682207\pi$
$491$	−5.78719e6	−1.08334	−0.541669	+	0.840592i	$0.682207\pi$
$492$	4.84602e6	0.902552
$493$	−1.36126e6	−0.252246
$494$	−274176.	−0.0505489
$495$	−2.24310e6	−0.411467
$496$	−265472.	−0.0484523
$497$	5.74241e6	1.04281
$498$	1.83350e6	0.331289
$499$	1.02912e6	0.185019	0.0925095	−	0.995712i	$-0.470511\pi$
$499$	1.02912e6	0.185019	0.0925095	+	0.995712i	$0.470511\pi$
$500$	2.62334e6	0.469278
$501$	9.78298e6	1.74131
$502$	2.51986e6	0.446290
$503$	−727370.	−0.128184	−0.0640922	−	0.997944i	$-0.520415\pi$
$503$	−727370.	−0.128184	−0.0640922	+	0.997944i	$0.520415\pi$
$504$	−8.80256e6	−1.54359
$505$	1.90421e6	0.332266
$506$	−939444.	−0.163115
$507$	1.04037e7	1.79750
$508$	1.39846e6	0.240432
$509$	−1.94630e6	−0.332977	−0.166489	−	0.986043i	$-0.553243\pi$
$509$	−1.94630e6	−0.332977	−0.166489	+	0.986043i	$0.553243\pi$
$510$	−4.10663e6	−0.699134
$511$	9.72624e6	1.64776
$512$	262144.	0.0441942
$513$	6.30054e6	1.05702
$514$	2.17634e6	0.363345
$515$	−5.76278e6	−0.957445
$516$	−26912.0	−0.00444961
$517$	1.04738e6	0.172336
$518$	−7.43636e6	−1.21769
$519$	3.38552e6	0.551705
$520$	−222208.	−0.0360372
$521$	−1.03133e7	−1.66457	−0.832286	−	0.554346i	$-0.812968\pi$
$521$	−1.03133e7	−1.66457	−0.832286	+	0.554346i	$0.812968\pi$
$522$	2.85126e6	0.457995
$523$	−6.86840e6	−1.09800	−0.548998	−	0.835823i	$-0.684991\pi$
$523$	−6.86840e6	−1.09800	−0.548998	+	0.835823i	$0.684991\pi$
$524$	4.24195e6	0.674897
$525$	−1.44339e7	−2.28552
$526$	−7.95734e6	−1.25402
$527$	1.18425e6	0.185746
$528$	−898304.	−0.140229
$529$	−2.66886e6	−0.414655
$530$	2.51943e6	0.389595
$531$	−1.27679e7	−1.96509
$532$	2.25216e6	0.345001
$533$	−1.16973e6	−0.178347
$534$	1.33123e7	2.02022
$535$	743070.	0.112239
$536$	3.07795e6	0.462754
$537$	554103.	0.0829191
$538$	7.01783e6	1.04532
$539$	4.36725e6	0.647495
$540$	5.10632e6	0.753570
$541$	1.00545e7	1.47695	0.738476	−	0.674280i	$-0.235546\pi$
$541$	1.00545e7	1.47695	0.738476	+	0.674280i	$0.235546\pi$
$542$	−6.63296e6	−0.969860
$543$	469133.	0.0682805
$544$	−1.16941e6	−0.169422
$545$	1.74611e6	0.251814
$546$	2.98816e6	0.428965
$547$	9.85725e6	1.40860	0.704299	−	0.709903i	$-0.251261\pi$
$547$	9.85725e6	1.40860	0.704299	+	0.709903i	$0.251261\pi$
$548$	3.93371e6	0.559566
$549$	2.81323e7	3.98359
$550$	−1.04738e6	−0.147637
$551$	−729504.	−0.102364
$552$	3.60250e6	0.503218
$553$	1.66543e7	2.31587
$554$	−170536.	−0.0236070
$555$	7.26662e6	1.00138
$556$	−5.81750e6	−0.798086
$557$	−1.45892e7	−1.99247	−0.996237	−	0.0866757i	$-0.972376\pi$
$557$	−1.45892e7	−1.99247	−0.996237	+	0.0866757i	$0.972376\pi$
$558$	−2.48050e6	−0.337252
$559$	6496.00	0.000879258 0
$560$	1.82528e6	0.245957
$561$	4.00728e6	0.537579
$562$	1.27804e6	0.170688
$563$	−1.02413e7	−1.36171	−0.680855	−	0.732418i	$-0.738392\pi$
$563$	−1.02413e7	−1.36171	−0.680855	+	0.732418i	$0.738392\pi$
$564$	−4.01638e6	−0.531664
$565$	8.11899e6	1.06999
$566$	−8.10939e6	−1.06401
$567$	−3.52454e7	−4.60410
$568$	−1.59789e6	−0.207814
$569$	−751816.	−0.0973489	−0.0486744	−	0.998815i	$-0.515500\pi$
$569$	−751816.	−0.0973489	−0.0486744	+	0.998815i	$0.515500\pi$
$570$	−2.20075e6	−0.283716
$571$	−7.01854e6	−0.900858	−0.450429	−	0.892812i	$-0.648729\pi$
$571$	−7.01854e6	−0.900858	−0.450429	+	0.892812i	$0.648729\pi$
$572$	216832.	0.0277098
$573$	−1.98747e7	−2.52879
$574$	9.60848e6	1.21724
$575$	4.20032e6	0.529801
$576$	2.44941e6	0.307613
$577$	−3.36377e6	−0.420617	−0.210308	−	0.977635i	$-0.567447\pi$
$577$	−3.36377e6	−0.420617	−0.210308	+	0.977635i	$0.567447\pi$
$578$	−462772.	−0.0576166
$579$	8.96947e6	1.11191
$580$	−591232.	−0.0729773
$581$	3.63538e6	0.446796
$582$	598444.	0.0732346
$583$	−2.45848e6	−0.299568
$584$	−2.70643e6	−0.328371
$585$	−2.07626e6	−0.250837
$586$	2.87538e6	0.345900
$587$	1.40585e7	1.68401	0.842006	−	0.539468i	$-0.181375\pi$
$587$	1.40585e7	1.68401	0.842006	+	0.539468i	$0.181375\pi$
$588$	−1.67472e7	−1.99755
$589$	634644.	0.0753775
$590$	2.64752e6	0.313119
$591$	3.50697e6	0.413013
$592$	2.06925e6	0.242666
$593$	−5.39420e6	−0.629927	−0.314963	−	0.949104i	$-0.601992\pi$
$593$	−5.39420e6	−0.629927	−0.314963	+	0.949104i	$0.601992\pi$
$594$	−4.98278e6	−0.579436
$595$	−8.14246e6	−0.942895
$596$	−892000.	−0.102861
$597$	−2.65505e7	−3.04886
$598$	−869568.	−0.0994376
$599$	−1.20204e7	−1.36883	−0.684417	−	0.729090i	$-0.739943\pi$
$599$	−1.20204e7	−1.36883	−0.684417	+	0.729090i	$0.739943\pi$
$600$	4.01638e6	0.455467
$601$	1.64636e6	0.185925	0.0929626	−	0.995670i	$-0.470366\pi$
$601$	1.64636e6	0.185925	0.0929626	+	0.995670i	$0.470366\pi$
$602$	−53360.0	−0.00600101
$603$	2.87596e7	3.22099
$604$	1.05027e6	0.117141
$605$	−453871.	−0.0504132
$606$	7.12542e6	0.788186
$607$	4.88451e6	0.538083	0.269041	−	0.963129i	$-0.413293\pi$
$607$	4.88451e6	0.538083	0.269041	+	0.963129i	$0.413293\pi$
$608$	−626688.	−0.0687531
$609$	7.95064e6	0.868678
$610$	−5.83346e6	−0.634748
$611$	969472.	0.105059
$612$	−1.09267e7	−1.17926
$613$	3.49011e6	0.375136	0.187568	−	0.982252i	$-0.439940\pi$
$613$	3.49011e6	0.375136	0.187568	+	0.982252i	$0.439940\pi$
$614$	−7.92568e6	−0.848429
$615$	−9.38916e6	−1.00101
$616$	−1.78112e6	−0.189122
$617$	9.12072e6	0.964531	0.482266	−	0.876025i	$-0.339814\pi$
$617$	9.12072e6	0.964531	0.482266	+	0.876025i	$0.339814\pi$
$618$	−2.15639e7	−2.27121
$619$	1.46635e7	1.53820	0.769098	−	0.639131i	$-0.220706\pi$
$619$	1.46635e7	1.53820	0.769098	+	0.639131i	$0.220706\pi$
$620$	514352.	0.0537380
$621$	1.99826e7	2.07933
$622$	−6.04120e6	−0.626105
$623$	2.63950e7	2.72460
$624$	−831488.	−0.0854859
$625$	1.67977e6	0.172009
$626$	8.00368e6	0.816307
$627$	2.14751e6	0.218155
$628$	−4.40587e6	−0.445793
$629$	−9.23079e6	−0.930277
$630$	1.70550e7	1.71198
$631$	−1.63870e7	−1.63842	−0.819212	−	0.573491i	$-0.805589\pi$
$631$	−1.63870e7	−1.63842	−0.819212	+	0.573491i	$0.805589\pi$
$632$	−4.63424e6	−0.461515
$633$	3.90282e6	0.387141
$634$	−1.03732e6	−0.102492
$635$	−2.70952e6	−0.266660
$636$	9.42755e6	0.924179
$637$	4.04242e6	0.394723
$638$	576928.	0.0561138
$639$	−1.49303e7	−1.44649
$640$	−507904.	−0.0490153
$641$	−3.26835e6	−0.314184	−0.157092	−	0.987584i	$-0.550212\pi$
$641$	−3.26835e6	−0.314184	−0.157092	+	0.987584i	$0.550212\pi$
$642$	2.78052e6	0.266249
$643$	8.32842e6	0.794393	0.397197	−	0.917734i	$-0.369983\pi$
$643$	8.32842e6	0.794393	0.397197	+	0.917734i	$0.369983\pi$
$644$	7.14288e6	0.678670
$645$	52142.0	0.00493501
$646$	2.79562e6	0.263570
$647$	2.49694e6	0.234503	0.117251	−	0.993102i	$-0.462592\pi$
$647$	2.49694e6	0.234503	0.117251	+	0.993102i	$0.462592\pi$
$648$	9.80742e6	0.917524
$649$	−2.58347e6	−0.240764
$650$	−969472.	−0.0900019
$651$	−6.91679e6	−0.639664
$652$	4.67104e6	0.430323
$653$	−789105.	−0.0724189	−0.0362094	−	0.999344i	$-0.511528\pi$
$653$	−789105.	−0.0724189	−0.0362094	+	0.999344i	$0.511528\pi$
$654$	6.53382e6	0.597341
$655$	−8.21878e6	−0.748521
$656$	−2.67366e6	−0.242576
$657$	−2.52882e7	−2.28562
$658$	−7.96352e6	−0.717035
$659$	−8.31393e6	−0.745749	−0.372874	−	0.927882i	$-0.621628\pi$
$659$	−8.31393e6	−0.745749	−0.372874	+	0.927882i	$0.621628\pi$
$660$	1.74046e6	0.155527
$661$	−4.33517e6	−0.385925	−0.192962	−	0.981206i	$-0.561810\pi$
$661$	−4.33517e6	−0.385925	−0.192962	+	0.981206i	$0.561810\pi$
$662$	204812.	0.0181640
$663$	3.70922e6	0.327716
$664$	−1.01158e6	−0.0890393
$665$	−4.36356e6	−0.382637
$666$	1.93345e7	1.68907
$667$	−2.31367e6	−0.201366
$668$	−5.39750e6	−0.468006
$669$	−1.35963e7	−1.17451
$670$	−5.96353e6	−0.513235
$671$	5.69232e6	0.488071
$672$	6.83008e6	0.583449
$673$	7.29313e6	0.620693	0.310346	−	0.950624i	$-0.399555\pi$
$673$	7.29313e6	0.620693	0.310346	+	0.950624i	$0.399555\pi$
$674$	1.06748e6	0.0905128
$675$	2.22784e7	1.88202
$676$	−5.73998e6	−0.483108
$677$	1.55814e7	1.30658	0.653288	−	0.757109i	$-0.273389\pi$
$677$	1.55814e7	1.30658	0.653288	+	0.757109i	$0.273389\pi$
$678$	3.03807e7	2.53819
$679$	1.18657e6	0.0987686
$680$	2.26573e6	0.187904
$681$	−7.97564e6	−0.659019
$682$	−501908.	−0.0413203
$683$	−2.16930e6	−0.177938	−0.0889690	−	0.996034i	$-0.528357\pi$
$683$	−2.16930e6	−0.177938	−0.0889690	+	0.996034i	$0.528357\pi$
$684$	−5.85562e6	−0.478556
$685$	−7.62157e6	−0.620609
$686$	−1.77431e7	−1.43953
$687$	1.86261e7	1.50567
$688$	14848.0	0.00119591
$689$	−2.27562e6	−0.182621
$690$	−6.97984e6	−0.558113
$691$	−1.32195e7	−1.05322	−0.526610	−	0.850107i	$-0.676537\pi$
$691$	−1.32195e7	−1.05322	−0.526610	+	0.850107i	$0.676537\pi$
$692$	−1.86787e6	−0.148280
$693$	−1.66423e7	−1.31638
$694$	2.49120e6	0.196341
$695$	1.12714e7	0.885149
$696$	−2.21235e6	−0.173114
$697$	1.19270e7	0.929932
$698$	9.74596e6	0.757157
$699$	4.36406e7	3.37830
$700$	7.96352e6	0.614271
$701$	−2.59395e7	−1.99373	−0.996866	−	0.0791122i	$-0.974791\pi$
$701$	−2.59395e7	−1.99373	−0.996866	+	0.0791122i	$0.974791\pi$
$702$	−4.61216e6	−0.353233
$703$	−4.94680e6	−0.377516
$704$	495616.	0.0376889
$705$	7.78174e6	0.589663
$706$	6.23828e6	0.471035
$707$	1.41280e7	1.06300
$708$	9.90686e6	0.742768
$709$	3.57531e6	0.267115	0.133557	−	0.991041i	$-0.457360\pi$
$709$	3.57531e6	0.267115	0.133557	+	0.991041i	$0.457360\pi$
$710$	3.09591e6	0.230485
$711$	−4.33012e7	−3.21237
$712$	−7.34470e6	−0.542968
$713$	2.01282e6	0.148279
$714$	−3.04686e7	−2.23669
$715$	−420112.	−0.0307326
$716$	−305712.	−0.0222859
$717$	8.83613e6	0.641895
$718$	7.67843e6	0.555855
$719$	−1.95814e6	−0.141261	−0.0706304	−	0.997503i	$-0.522501\pi$
$719$	−1.95814e6	−0.141261	−0.0706304	+	0.997503i	$0.522501\pi$
$720$	−4.74573e6	−0.341171
$721$	−4.27561e7	−3.06309
$722$	−8.40622e6	−0.600147
$723$	−3.68824e7	−2.62406
$724$	−258832.	−0.0183515
$725$	−2.57949e6	−0.182259
$726$	−1.69836e6	−0.119588
$727$	1.55360e7	1.09019	0.545095	−	0.838374i	$-0.316493\pi$
$727$	1.55360e7	1.09019	0.545095	+	0.838374i	$0.316493\pi$
$728$	−1.64864e6	−0.115292
$729$	1.90893e7	1.33036
$730$	5.24371e6	0.364193
$731$	−66236.0	−0.00458459
$732$	−2.18284e7	−1.50572
$733$	−1.46002e7	−1.00369	−0.501844	−	0.864958i	$-0.667345\pi$
$733$	−1.46002e7	−1.00369	−0.501844	+	0.864958i	$0.667345\pi$
$734$	1.44490e7	0.989915
$735$	3.24476e7	2.21546
$736$	−1.98758e6	−0.135248
$737$	5.81925e6	0.394638
$738$	−2.49820e7	−1.68845
$739$	−2.06682e7	−1.39217	−0.696085	−	0.717959i	$-0.745077\pi$
$739$	−2.06682e7	−1.39217	−0.696085	+	0.717959i	$0.745077\pi$
$740$	−4.00917e6	−0.269138
$741$	1.98778e6	0.132991
$742$	1.86926e7	1.24640
$743$	1.17065e7	0.777953	0.388976	−	0.921248i	$-0.372829\pi$
$743$	1.17065e7	0.777953	0.388976	+	0.921248i	$0.372829\pi$
$744$	1.92467e6	0.127475
$745$	1.72825e6	0.114082
$746$	1.57587e7	1.03675
$747$	−9.45199e6	−0.619757
$748$	−2.21091e6	−0.144483
$749$	5.51310e6	0.359080
$750$	−1.90192e7	−1.23464
$751$	−1.27607e7	−0.825610	−0.412805	−	0.910819i	$-0.635451\pi$
$751$	−1.27607e7	−0.825610	−0.412805	+	0.910819i	$0.635451\pi$
$752$	2.21594e6	0.142894
$753$	−1.82690e7	−1.17416
$754$	534016.	0.0342079
$755$	−2.03490e6	−0.129920
$756$	3.78856e7	2.41085
$757$	−1.40869e7	−0.893458	−0.446729	−	0.894669i	$-0.647411\pi$
$757$	−1.40869e7	−0.893458	−0.446729	+	0.894669i	$0.647411\pi$
$758$	−8.75316e6	−0.553339
$759$	6.81097e6	0.429145
$760$	1.21421e6	0.0762534
$761$	2.33822e7	1.46360	0.731801	−	0.681518i	$-0.238680\pi$
$761$	2.33822e7	1.46360	0.731801	+	0.681518i	$0.238680\pi$
$762$	−1.01389e7	−0.632560
$763$	1.29550e7	0.805611
$764$	1.09653e7	0.679655
$765$	2.11704e7	1.30790
$766$	3.07355e6	0.189264
$767$	−2.39131e6	−0.146774
$768$	−1.90054e6	−0.116272
$769$	−1.09575e7	−0.668185	−0.334092	−	0.942540i	$-0.608430\pi$
$769$	−1.09575e7	−0.668185	−0.334092	+	0.942540i	$0.608430\pi$
$770$	3.45092e6	0.209753
$771$	−1.57785e7	−0.955938
$772$	−4.94867e6	−0.298845
$773$	1.69336e7	1.01930	0.509648	−	0.860383i	$-0.329776\pi$
$773$	1.69336e7	1.01930	0.509648	+	0.860383i	$0.329776\pi$
$774$	138736.	0.00832409
$775$	2.24407e6	0.134209
$776$	−330176.	−0.0196830
$777$	5.39136e7	3.20366
$778$	1.29725e6	0.0768379
$779$	6.39173e6	0.377376
$780$	1.61101e6	0.0948115
$781$	−3.02101e6	−0.177225
$782$	8.86649e6	0.518483
$783$	−1.22716e7	−0.715316
$784$	9.23981e6	0.536875
$785$	8.53638e6	0.494424
$786$	−3.07542e7	−1.77561
$787$	−7.51655e6	−0.432595	−0.216298	−	0.976327i	$-0.569398\pi$
$787$	−7.51655e6	−0.432595	−0.216298	+	0.976327i	$0.569398\pi$
$788$	−1.93488e6	−0.111004
$789$	5.76907e7	3.29923
$790$	8.97884e6	0.511862
$791$	6.02377e7	3.42316
$792$	4.63091e6	0.262333
$793$	5.26893e6	0.297536
$794$	1.33903e6	0.0753771
$795$	−1.82659e7	−1.02500
$796$	1.46486e7	0.819432
$797$	3.93788e6	0.219592	0.109796	−	0.993954i	$-0.464980\pi$
$797$	3.93788e6	0.219592	0.109796	+	0.993954i	$0.464980\pi$
$798$	−1.63282e7	−0.907674
$799$	−9.88515e6	−0.547793
$800$	−2.21594e6	−0.122414
$801$	−6.86271e7	−3.77932
$802$	−3.60809e6	−0.198080
$803$	−5.11685e6	−0.280036
$804$	−2.23152e7	−1.21747
$805$	−1.38393e7	−0.752706
$806$	−464576.	−0.0251895
$807$	−5.08793e7	−2.75015
$808$	−3.93126e6	−0.211838
$809$	−1.73609e7	−0.932612	−0.466306	−	0.884624i	$-0.654415\pi$
$809$	−1.73609e7	−0.932612	−0.466306	+	0.884624i	$0.654415\pi$
$810$	−1.90019e7	−1.01762
$811$	2.70850e7	1.44603	0.723014	−	0.690833i	$-0.242756\pi$
$811$	2.70850e7	1.44603	0.723014	+	0.690833i	$0.242756\pi$
$812$	−4.38656e6	−0.233472
$813$	4.80890e7	2.55164
$814$	3.91217e6	0.206946
$815$	−9.05014e6	−0.477267
$816$	8.47821e6	0.445737
$817$	−35496.0	−0.00186048
$818$	−2.00183e7	−1.04603
$819$	−1.54045e7	−0.802486
$820$	5.18022e6	0.269038
$821$	3.59384e7	1.86080	0.930402	−	0.366540i	$-0.119458\pi$
$821$	3.59384e7	1.86080	0.930402	+	0.366540i	$0.119458\pi$
$822$	−2.85194e7	−1.47218
$823$	−505509.	−0.0260153	−0.0130077	−	0.999915i	$-0.504141\pi$
$823$	−505509.	−0.0260153	−0.0130077	+	0.999915i	$0.504141\pi$
$824$	1.18973e7	0.610425
$825$	7.59348e6	0.388424
$826$	1.96429e7	1.00174
$827$	−2.99955e7	−1.52508	−0.762539	−	0.646942i	$-0.776048\pi$
$827$	−2.99955e7	−1.52508	−0.762539	+	0.646942i	$0.776048\pi$
$828$	−1.85715e7	−0.941393
$829$	2.96942e7	1.50067	0.750334	−	0.661059i	$-0.229893\pi$
$829$	2.96942e7	1.50067	0.750334	+	0.661059i	$0.229893\pi$
$830$	1.95994e6	0.0987526
$831$	1.23639e6	0.0621086
$832$	458752.	0.0229757
$833$	−4.12182e7	−2.05815
$834$	4.21769e7	2.09971
$835$	1.04577e7	0.519061
$836$	−1.18483e6	−0.0586329
$837$	1.06759e7	0.526734
$838$	−1.20049e7	−0.590541
$839$	−1.41371e7	−0.693356	−0.346678	−	0.937984i	$-0.612690\pi$
$839$	−1.41371e7	−0.693356	−0.346678	+	0.937984i	$0.612690\pi$
$840$	−1.32333e7	−0.647097
$841$	−1.90903e7	−0.930727
$842$	1.82490e7	0.887070
$843$	−9.26579e6	−0.449069
$844$	−2.15328e6	−0.104051
$845$	1.11212e7	0.535810
$846$	2.07052e7	0.994609
$847$	−3.36743e6	−0.161284
$848$	−5.20141e6	−0.248388
$849$	5.87931e7	2.79935
$850$	9.88515e6	0.469284
$851$	−1.56891e7	−0.742633
$852$	1.15847e7	0.546746
$853$	−4.68539e6	−0.220482	−0.110241	−	0.993905i	$-0.535162\pi$
$853$	−4.68539e6	−0.220482	−0.110241	+	0.993905i	$0.535162\pi$
$854$	−4.32805e7	−2.03071
$855$	1.13453e7	0.530761
$856$	−1.53408e6	−0.0715589
$857$	−4.12846e7	−1.92015	−0.960076	−	0.279740i	$-0.909752\pi$
$857$	−4.12846e7	−1.92015	−0.960076	+	0.279740i	$0.909752\pi$
$858$	−1.57203e6	−0.0729026
$859$	−3.54805e6	−0.164062	−0.0820308	−	0.996630i	$-0.526141\pi$
$859$	−3.54805e6	−0.164062	−0.0820308	+	0.996630i	$0.526141\pi$
$860$	−28768.0	−0.00132637
$861$	−6.96615e7	−3.20247
$862$	1.95913e7	0.898039
$863$	−3.07605e7	−1.40594	−0.702970	−	0.711219i	$-0.748143\pi$
$863$	−3.07605e7	−1.40594	−0.702970	+	0.711219i	$0.748143\pi$
$864$	−1.05421e7	−0.480443
$865$	3.61900e6	0.164456
$866$	2.69150e7	1.21955
$867$	3.35510e6	0.151585
$868$	3.81616e6	0.171920
$869$	−8.76161e6	−0.393581
$870$	4.28643e6	0.191998
$871$	5.38642e6	0.240577
$872$	−3.60486e6	−0.160545
$873$	−3.08508e6	−0.137003
$874$	4.75157e6	0.210406
$875$	−3.77106e7	−1.66511
$876$	1.96216e7	0.863923
$877$	3.05535e7	1.34141	0.670706	−	0.741723i	$-0.265991\pi$
$877$	3.05535e7	1.34141	0.670706	+	0.741723i	$0.265991\pi$
$878$	−1.34013e7	−0.586695
$879$	−2.08465e7	−0.910040
$880$	−960256.	−0.0418004
$881$	4.21018e7	1.82751	0.913757	−	0.406262i	$-0.133168\pi$
$881$	4.21018e7	1.82751	0.913757	+	0.406262i	$0.133168\pi$
$882$	8.63345e7	3.73691
$883$	57164.0	0.00246729	0.00123365	−	0.999999i	$-0.499607\pi$
$883$	57164.0	0.00246729	0.00123365	+	0.999999i	$0.499607\pi$
$884$	−2.04646e6	−0.0880792
$885$	−1.91945e7	−0.823796
$886$	−2.84974e7	−1.21961
$887$	−1.16106e7	−0.495504	−0.247752	−	0.968824i	$-0.579692\pi$
$887$	−1.16106e7	−0.495504	−0.247752	+	0.968824i	$0.579692\pi$
$888$	−1.50020e7	−0.638437
$889$	−2.01029e7	−0.853109
$890$	1.42304e7	0.602200
$891$	1.85422e7	0.782467
$892$	7.50142e6	0.315669
$893$	−5.29747e6	−0.222300
$894$	6.46700e6	0.270619
$895$	592317.	0.0247170
$896$	−3.76832e6	−0.156811
$897$	6.30437e6	0.261614
$898$	−1.08371e7	−0.448460
$899$	−1.23610e6	−0.0510101
$900$	−2.07052e7	−0.852064
$901$	2.32032e7	0.952215
$902$	−5.05490e6	−0.206869
$903$	386860.	0.0157883
$904$	−1.67618e7	−0.682181
$905$	501487.	0.0203535
$906$	−7.61447e6	−0.308191
$907$	2.09855e7	0.847034	0.423517	−	0.905888i	$-0.360795\pi$
$907$	2.09855e7	0.847034	0.423517	+	0.905888i	$0.360795\pi$
$908$	4.40035e6	0.177122
$909$	−3.67327e7	−1.47450
$910$	3.19424e6	0.127869
$911$	4.74125e7	1.89277	0.946383	−	0.323047i	$-0.104707\pi$
$911$	4.74125e7	1.89277	0.946383	+	0.323047i	$0.104707\pi$
$912$	4.54349e6	0.180885
$913$	−1.91253e6	−0.0759330
$914$	9.65445e6	0.382263
$915$	4.22926e7	1.66998
$916$	−1.02765e7	−0.404675
$917$	−6.09781e7	−2.39470
$918$	4.70276e7	1.84181
$919$	4.04326e7	1.57922	0.789610	−	0.613609i	$-0.210283\pi$
$919$	4.04326e7	1.57922	0.789610	+	0.613609i	$0.210283\pi$
$920$	3.85094e6	0.150002
$921$	5.74612e7	2.23216
$922$	−2.62426e7	−1.01667
$923$	−2.79630e6	−0.108039
$924$	1.29131e7	0.497567
$925$	−1.74916e7	−0.672164
$926$	−1.88968e7	−0.724205
$927$	1.11166e8	4.24885
$928$	1.22061e6	0.0465271
$929$	3.30757e7	1.25739	0.628694	−	0.777652i	$-0.283590\pi$
$929$	3.30757e7	1.25739	0.628694	+	0.777652i	$0.283590\pi$
$930$	−3.72905e6	−0.141381
$931$	−2.20889e7	−0.835219
$932$	−2.40776e7	−0.907973
$933$	4.37987e7	1.64724
$934$	−9.13776e6	−0.342746
$935$	4.28364e6	0.160245
$936$	4.28646e6	0.159922
$937$	−3.15132e7	−1.17258	−0.586292	−	0.810100i	$-0.699413\pi$
$937$	−3.15132e7	−1.17258	−0.586292	+	0.810100i	$0.699413\pi$
$938$	−4.42456e7	−1.64196
$939$	−5.80267e7	−2.14765
$940$	−4.29338e6	−0.158482
$941$	−9.54147e6	−0.351270	−0.175635	−	0.984455i	$-0.556198\pi$
$941$	−9.54147e6	−0.351270	−0.175635	+	0.984455i	$0.556198\pi$
$942$	3.19426e7	1.17285
$943$	2.02718e7	0.742358
$944$	−5.46586e6	−0.199631
$945$	−7.34034e7	−2.67385
$946$	28072.0	0.00101987
$947$	2.24208e7	0.812410	0.406205	−	0.913782i	$-0.366852\pi$
$947$	2.24208e7	0.812410	0.406205	+	0.913782i	$0.366852\pi$
$948$	3.35982e7	1.21422
$949$	−4.73626e6	−0.170714
$950$	5.29747e6	0.190441
$951$	7.52060e6	0.269650
$952$	1.68102e7	0.601148
$953$	1.68985e7	0.602720	0.301360	−	0.953510i	$-0.402559\pi$
$953$	1.68985e7	0.602720	0.301360	+	0.953510i	$0.402559\pi$
$954$	−4.86007e7	−1.72891
$955$	−2.12453e7	−0.753798
$956$	−4.87510e6	−0.172520
$957$	−4.18273e6	−0.147632
$958$	3.80618e6	0.133991
$959$	−5.65471e7	−1.98547
$960$	3.68230e6	0.128956
$961$	−2.75538e7	−0.962438
$962$	3.62118e6	0.126157
$963$	−1.43341e7	−0.498085
$964$	2.03489e7	0.705260
$965$	9.58805e6	0.331445
$966$	−5.17859e7	−1.78554
$967$	−3.06946e7	−1.05559	−0.527796	−	0.849371i	$-0.676982\pi$
$967$	−3.06946e7	−1.05559	−0.527796	+	0.849371i	$0.676982\pi$
$968$	937024.	0.0321412
$969$	−2.02682e7	−0.693436
$970$	639716.	0.0218302
$971$	3.35664e7	1.14250	0.571251	−	0.820776i	$-0.306458\pi$
$971$	3.35664e7	1.14250	0.571251	+	0.820776i	$0.306458\pi$
$972$	−3.10769e7	−1.05505
$973$	8.36266e7	2.83180
$974$	1.40594e7	0.474863
$975$	7.02867e6	0.236789
$976$	1.20433e7	0.404687
$977$	2.47897e7	0.830873	0.415436	−	0.909622i	$-0.363629\pi$
$977$	2.47897e7	0.830873	0.415436	+	0.909622i	$0.363629\pi$
$978$	−3.38650e7	−1.13215
$979$	−1.38861e7	−0.463045
$980$	−1.79021e7	−0.595442
$981$	−3.36829e7	−1.11747
$982$	−2.31488e7	−0.766036
$983$	5.22606e6	0.172501	0.0862503	−	0.996274i	$-0.472512\pi$
$983$	5.22606e6	0.172501	0.0862503	+	0.996274i	$0.472512\pi$
$984$	1.93841e7	0.638200
$985$	3.74883e6	0.123113
$986$	−5.44506e6	−0.178365
$987$	5.77355e7	1.88647
$988$	−1.09670e6	−0.0357435
$989$	−112578.	−0.00365985
$990$	−8.97239e6	−0.290951
$991$	2.40826e7	0.778967	0.389484	−	0.921033i	$-0.372653\pi$
$991$	2.40826e7	0.778967	0.389484	+	0.921033i	$0.372653\pi$
$992$	−1.06189e6	−0.0342610
$993$	−1.48489e6	−0.0477882
$994$	2.29696e7	0.737375
$995$	−2.83816e7	−0.908823
$996$	7.33398e6	0.234256
$997$	−1.32606e7	−0.422499	−0.211249	−	0.977432i	$-0.567753\pi$
$997$	−1.32606e7	−0.422499	−0.211249	+	0.977432i	$0.567753\pi$
$998$	4.11650e6	0.130828
$999$	−8.32145e7	−2.63806

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.6.a.c.1.1	✓	1
3.2	odd	2		198.6.a.b.1.1		1
4.3	odd	2		176.6.a.e.1.1		1
5.2	odd	4		550.6.b.a.199.2		2
5.3	odd	4		550.6.b.a.199.1		2
5.4	even	2		550.6.a.c.1.1		1
7.6	odd	2		1078.6.a.f.1.1		1
8.3	odd	2		704.6.a.a.1.1		1
8.5	even	2		704.6.a.j.1.1		1
11.10	odd	2		242.6.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.6.a.c.1.1	✓	1	1.1	even	1	trivial
176.6.a.e.1.1		1	4.3	odd	2
198.6.a.b.1.1		1	3.2	odd	2
242.6.a.a.1.1		1	11.10	odd	2
550.6.a.c.1.1		1	5.4	even	2
550.6.b.a.199.1		2	5.3	odd	4
550.6.b.a.199.2		2	5.2	odd	4
704.6.a.a.1.1		1	8.3	odd	2
704.6.a.j.1.1		1	8.5	even	2
1078.6.a.f.1.1		1	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	22.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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